Electron equivalent

3(b) Equivalent electrons The Russell-Saunders coupling scheme for two, or more, equivalent electrons (i.e. with the same n and f) is rather more lengthy to apply. We shall use the example of two equivalent p electrons, as in the ground configuration of carbon  

for the filled orbitals L = 0 and 5 = 0, so we have to consider only the 2p electrons. Since n = 2 and f = 1 for both electrons the Pauli exclusion principle is in danger of being violated unless the two electrons have different values of either or m. For non-equivalent electrons we do not have to consider the values of these two quantum numbers because, as either n or f is different for the electrons, there is no danger of violation. 

If should be nofed fhaf fhe indisfinguishabilify of fhe elections has been faken info accounf in fhe fable so fhaf, for example, fhe combination (m )i = (m )2 = f, =, =  

If is inferesfing fo nofe fhaf of fhe 5, S, P, P, and farms which arise from two non-equivalent p electrons, as in the s 2s 2p 3p configuration of fhe carbon atom, only 5, 

It is unfortunately the case, however, that P, for example, is sometimes referred to as a state. 

For one of the 2p electrons, which we shall label 1, we have lx = 1 and (me)l = +1, 0 or — 1 and, in addition,. v, = j, and (ms)l = +( or —j, similarly, for electron 2. The Pauli exclusion principle requires that the pair of quantum numbers (me)1 and (ms)l cannot simultaneously have the same values as (me)2 and (ms)2. The result is that there are fifteen allowed combinations of values and they are all given in Table 7.3. 

It should be noted that the indistinguishability of the electrons has been taken into account in the table so that, for example, the combination (me)1 = (ml)2 = 1, (ms)1 = —, (ms)2 = cannot be included in addition to (me) = mt)2 = 1, (wjj = j, (ms)2 = — which is obtained from the first by electron exchange. 

---

Covalent bonds are formed by the sharing of electrons. Thus the carbon atom, with four equivalent electrons shares with the electrons from four hydrogen atoms. 

A decrease of a- and tt-electronic density in both adjacent positions. For the a system this decrease is approximately the same at the 2- and 4-positions, which expresses an equivalent electron withdrawing from nitrogen in both positions. On the other hand, the decrease in tr-electronic density is twice as large at C-2 as at C-4. 

First we consider, for non-equivalent electrons, the strong coupling between orbital angular momenta, referred to as it coupling, using a particular example. 

In a similar way the coupling of a third vector to any of the L in Figure 7.4(a) will give the terms arising from three non-equivalent electrons, and so on. 

Table 7.2 lists the terms that arise from various combinations of two non-equivalent electrons. 

Table 7.2 Terms arising from some configurations of non-equivalent and equivalent electrons...

Of the terms arising from equivalent electrons those with the highest multiplicity lie lowest in energy. 

There are two further rules for ground terms which tell us whether a multiplet arising from equivalent electrons is normal or inverted. 

Normal multiplets arise from equivalent electrons when a partially filled orbital is less than half full. 

In the excited electron configuration given, there are two electrons in partly filled orbitals, a Ad (electron 1) and a 5/ electron (electron 2). These are non-equivalent electrons (Section 7.1.2.3a) and we need consider only the coupling of the orbital angular momenta, fj andf2> and the spin angular momenta, Sj and S2-... 

Pyrazole Equivalent Electron-withdrawing group prefers 3-position... 

FIGURE 25.1 The citrate-malate-pyruvate shuttle provides cytosolic acetate units and reducing equivalents (electrons) for fatty acid synthesis. The shuttle collects carbon substrates, primarily from glycolysis but also from fatty acid oxidation and amino acid catabolism. Most of the reducing equivalents are glycolytic in origin. Pathways that provide carbon for fatty acid synthesis are shown in blue pathways that supply electrons for fatty acid synthesis are shown in red. 

NADPH can be produced in the pentose phosphate pathway as well as by malic enzyme (Figure 25.1). Reducing equivalents (electrons) derived from glycolysis in the form of NADH can be transformed into NADPH by the combined action of malate dehydrogenase and malic enzyme ... 

Let us now derive the Slater-Kirkwood38 formula in terms of our present quantities. A single subshell of equivalent electrons is assumed. Equation 29 may be rearranged to... 

The bond diagrams provide an obvious simple method of determining the allowed spectral terms for equivalent electrons with Russell-Saunders coupling, which may be convenient for the reason that it separates states of different multiplicity at the start. 

In contrast to the transition metals, where there is often a change in oxidation level at the metal during the reaction, there is usually no change in oxidation level for boron, silicon, and tin compounds. The synthetically important reactions of these three groups of compounds involve transfer of a carbon substituent with one (radical equivalent) or two (carbanion equivalent) electrons to a reactive carbon center. Here we focus on the nonradical reactions and deal with radical reactions in Chapter 10. We have already introduced one important aspect of boron and tin chemistry in the transmetallation reactions involved in Pd-catalyzed cross-coupling reactions, discussed... 

The state with the highest multiplicity gives the lowest energy for equivalent electrons. 

Table 2.6 Spectroscopic States Arising for Equivalent Electrons. ...

The MALATE-ASPARTATE SHUTTLE gets reducing equivalents (electrons) from cytosolic NADH into the mitochondria so that 3 ATPs can be made. 

Thoriated tungsten, whose surface has been carburized at high temperatures, have lower work functions than pure tungsten and emit equivalent electron beam currents at lower temperatures thereby extending the life and stability when compared to regular tungsten sources. These sources require a stable, high vacuum (10 to 10 torr) and are more difficult to fabricate. 

When in the valence configuration of the atomic system there are N equivalent electrons expressions (9) and (17) should be multiplied by N and by the appropriate Coefficient of Fractional Parentage (CFP) [10,12], In all the present transitions N has been taken equal to 5, as it is one of the five 3p electrons the one that experiences the transition. The CFP varies with the initial and final states. All the CFP values have been taken from Ref. 12. 

As in the case of LS coupling, when there are N equivalent electrons in the outer shell, both the line strength and the oscillator strength should be multiplied by N as well as by the corresponding CFP [ 10,12]. As in the LS scheme the two forms of the electric dipole length transition operator have been employed here in the calculation of the radial transition integral, I nl, n l ). 

As the electrons are indistinguishable in the antisymmetrized wave function, the one-electron scattering can be obtained by integration over all coordinates but those of they th electron. Summation over all equivalent electrons then leads to... 

Photon Experiment Equivalent Electron-Impact Experiment... 

---